Simplify the following expression: $p = \dfrac{-5q^2 + 5q + 360}{q + 8} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ p =\dfrac{-5(q^2 - 1q - 72)}{q + 8} $ Then we factor the remaining polynomial: $q^2 {-1}q {-72} $ ${8} {-9} = {-1}$ ${8} \times {-9} = {-72}$ $ (q + {8}) (q {-9}) $ This gives us a factored expression: $\dfrac{-5(q + {8}) (q {-9})}{q + 8}$ We can divide the numerator and denominator by $(q - 8)$ on condition that $q \neq -8$ Therefore $p = -5(q - 9); q \neq -8$